Conventional operational amplifiers have a differential input stage driven by a positive (non-inverting) and a negative (inverting) input connected to an output stage. Direct-coupled high gain amplifiers of this type are typically used in a feedback loop to implement a given function determined by extrinsic discrete components such as, for example, resistors and diodes. Operational amplifiers, properly configured, can even perform many mathematical operations, thus the name operational amplifier. In addition, operational amplifier circuits can be configured using external discrete components, either singly or in combination to generate specific output signals. Among these configurations, two of the most important and useful are limiters and rectifiers.
Prior art full-wave rectifiers generally use two operational amplifiers as shown in FIG. 1. More specifically, a resistor 3, a resistor 4 and the cathode of a diode 9 are connected to an inverting input of an operational amplifier 1 whose non-inverting input is connected to a reference potential point 12. The other end of the resistor 3 is connected to an input terminal 10 and to a resistor 5; and the other end of the resistor 4 is connected to the anode of a diode 8 and to a resistor 6. The cathode of the diode 8 is connected to the output of the operational amplifier 1 and to the anode of diode 9; and the other end of the resistor 6 is connected to an inverting input of an operational amplifier 2 and to a resistor 7. The non-inverting input of the operational amplifier 2 is connected to a reference potential 12'. The other end of the resistor 7 is connected to the output of the operational amplifier 2 and to an output terminal 11.
The operation of the rectifier in the prior art will now be discussed. When a positive input voltage V.sub.INA is applied to the input terminal 10, the diode 8 is rendered conductive and the diode 9 is rendered nonconductive. The operational amplifier 1 operates as a feedback amplifier having an amplification factor defined by resistors 3 and 4. If the resistances of the resistors 3 and 4 are denoted by R.sub.3 and R.sub.4, the output voltage V.sub.OUTD at the point D is given by the following equation (1), ##EQU1##
Here the electric currents flowing through the resistors 5, 6 and 7 are denoted by I.sub.5, I.sub.6 and I.sub.7. If operational amplifiers 1 and 2 have infinitely great input impedances and, since the potentials at the inputs B and E of the operational amplifiers 1 and 2 can be assumed to be the same as the reference potential, the electric currents I.sub.5 and I.sub.6 are given by the following equations (2) and (3), ##EQU2## where R.sub.5 and R.sub.6 denote resistances of the resistors 5 and 6.
Furthermore, the following equation (4) holds true among the electric currents I.sub.5, I.sub.6 and I.sub.7, EQU I.sub.7 =I.sub.5 +I.sub.6 ( 4)
If the equations (2) and (3) are substituted for the equation (4), the current I.sub.7 is given by the equation (5), ##EQU3##
If the equation (1) is substituted for the equation (5), the current I.sub.7 is given by the equation (6), ##EQU4##
Here, if the output voltage at the output point F of the operational amplifier 2 is denoted by V.sub.OUTF1 and the resistance of the resistor 7 by R.sub.7, the voltage V.sub.OUTF1 at the output point F is expressed by the equation (7), EQU V.sub.OUTF1 =R.sub.7 .times.I.sub.7 ( 7)
Hence, if the equation (6) is substituted for the equation (7), there holds the following equation (8), ##EQU5##
If the following equations (9) and (10) hold, the equation (8) can be replaced by the equation (11), ##EQU6##
Therefore, when a positive input voltage V.sub.INA is applied to the input terminal 10, the same positive input voltage V.sub.INA appears on the output point F of the operational amplifier 2, i.e., appears on the output terminal 11, provided the above-mentioned resistances are set according to equations (9) and (10).
Next, when a negative input voltage V'.sub.INA =-V.sub.INA is applied to the terminal 10, the diode 8 is rendered nonconductive, and the diode 9 is rendered conductive. Consequently, the potential becomes zero at the point D, resulting in no voltage drop across the resistor 6, i.e., both terminals of the resistor 6 are held at the reference potential, and no current flows through the resistor 6.
From the equations (4) and (5), therefore, the equation (12) holds true. ##EQU7##
Therefore, the output voltage V.sub.OUTF2 at the output point F of the operational amplifier 2 is given by the equation (13), ##EQU8##
Hence, if the equation (10) holds, the equation (13) is rewritten as, ##EQU9##
Therefore, when the negative input voltage V'.sub.INA (-V.sub.INA) is applied to the input terminal 10, a voltage of the same voltage level but having an inverted sign, i.e., the voltage V.sub.INA, is obtained from the output point F of the operational amplifier or from the output terminal 11.
Thus, the circuit of FIG. 1 operates as an absolute value circuit which always produces output voltages of positive polarity upon receipt of input voltages of both positive and negative polarities. That is, when signals of sinusoidal waveform, such as shown in FIG. 2(a) are input to the input terminal 10, the output terminal 11 produces signals in which the positive portions of the input sinusoidal waves are output in their original form while the negative portions are output after they are inverted to positive portions as shown in FIG. 2(b). In other words, the circuit in the prior art operates as a full-wave rectifier. The conventional rectifier circuit shown in FIG. 1, however, requires five resistors having accurate resistances, two diodes and two operational amplifiers, i.e., two amplifier circuits, and further must satisfy the requirements of equations (9) and (10) for the five resistors. To realize a rectifying circuit, therefore, a considerable number of elements must be used, and it is necessary to maintain very high accuracy in the resistance values of the five resistors. Moreover, the speed of the circuit shown in FIG. 1 is limited due to the usually problematic recovery time of the diodes and the operational amplifier slew rates when the input signal changes sign.
Conventional prior art limiter circuits are also susceptible to the problems described above. A limiter, in its ideal basic form, constrains a signal to be below or above a particular specified value or breakpoint. The output signal is proportional to the input below (or above) this breakpoint and stays constant for inputs above (or below) this value.
An example of a prior art lower limit limiter circuit is shown in FIG. 3. The operation of this circuit will be described with reference to the components and circuit shown in FIG. 3. Due to the presence of the diode 19, connected between points H and J, this circuit is analyzed by considering the operation of two cases: the first is when the diode 19 is assumed to be an open circuit; and the second is when the diode 19 is considered to be a short circuit.
When the diode 19 in the circuit shown by FIG. 3 is not conducting, the circuit operates as an inverting amplifier with the output given by equation (15), EQU v.sub.o =-v.sub.ix (R.sub.f /R.sub.A) (15)
where the resistors R.sub.F and R.sub.A correspond to resistors 18 and 16 respectively, the gain is -R.sub.F /R.sub.A. To find the breakpoint, we must solve for v.sub.1 as follows: ##EQU10## where V.sub.ref is limiting reference voltage input at point 24, and v.sub.o is the output voltage measured at point 23 and R.sub.1 and R.sub.2 correspond to resistors 20 and 21 respectively.
The diode 19 conducts when v.sub.1 tries to go below a predetermined voltage. Solving the above equations for this situation results in the equation (17), ##EQU11## This represents the breakpoint between the two circuit conditions. FIG. 4(a) shows an exemplary sinusoidal input waveform input to terminal 22, which is connected to resistor 16 which is, in turn, connected to the inverting input of the operational amplifier 15. A feedback loop is realized between the output of the operational amplifier 15 and is connected between points I and H through resistor 18. The non-inverting input of the operational amplifier 15 is connected to a reference potential 25 through resistor 17. The diode 19 is connected between points H and J. FIG. 4(b) shows the output of the lower limiter wherein the voltage output matches the input for voltages greater than the limiting reference voltage and remains constant for those periods where the input voltage falls below the limiting reference voltage. A maximum voltage limiter is simply the same circuit shown in FIG. 3 but having the diode 19 oriented in the opposite direction.
As shown in the above description, conventional limiter circuits suffer from the same performance inefficiencies as the full-wave rectifier circuit described above.